Easy-to-use gravity-driven step emulsification devices are capable of digital enumeration of bacteria and antibiotic susceptibility testing within 5 hours.

Thermal motion of particles and molecules in liquids underlies many chemical and biological processes. Liquids, especially in biology, are complex due to structure at multiple relevant length scales. While diffusion in homogeneous simple liquids is well understood through the Stokes–Einstein relation, this equation fails completely in describing diffusion in complex media. Modeling, understanding, engineering and controlling processes at the nanoscale, most importantly inside living cells, requires a theoretical framework for the description of viscous response to allow predictions of diffusion rates in complex fluids. Here we use a general framework with the viscosity η(k) described by a function of wave vector in reciprocal space. We introduce a formulation that allows one to relate the rotational and translational diffusion coefficients and determine the viscosity η(k) directly from experiments. We apply our theory to provide a database for rotational diffusion coefficients of proteins/protein complexes in the bacterium E. coli. We also provide a database for the diffusion coefficient of proteins sliding along major grooves of DNA in E. coli. These parameters allow predictions of rate constants for association of proteins. In addition to constituting a theoretical framework for description of diffusion of probes and viscosity in complex fluids, the formulation that we propose should decrease substantially the cost of numerical simulations of transport in complex media by replacing the simulation of individual crowding particles with a continuous medium characterized by a wave-length dependent viscosity η(k).

There is a long-standing question as to whether and to what extent it is possible to describe nonequilibrium systems in stationary states in terms of global thermodynamic functions. The positive answers have been obtained only for isothermal systems or systems with small temperature differences. We formulate thermodynamics of the stationary states of the ideal gas subjected to heat flow in the form of the zeroth, first, and second law. Surprisingly, the formal structure of steady state thermodynamics is the same as in equilibrium thermodynamics. We rigorously show that U satisfies the following equation dU = T*dS* − pdV for a constant number of particles, irrespective of the shape of the container, boundary conditions, the size of the system, or the mode of heat transfer into the system. We calculate S* and T* explicitly. The theory selects stable nonequilibrium steady states in a multistable system of ideal gas subjected to volumetric heating. It reduces to equilibrium thermodynamics when heat flux goes to zero.

Microfluidic step emulsification passively produces highly monodisperse droplets and can be easily parallelized for high throughput emulsion production. The two main techniques used for step emulsification are: i) edge-based droplet generation (EDGE), where droplets are formed in a single, very wide and shallow nozzle, and ii) microchannel emulsification (MCE), where droplets are formed in many separated narrow nozzles. These techniques differ in modes of droplet formation that influence the throughput and monodispersity of produced emulsions. Here we report a systematic study of novel grooved step emulsifying geometries, a hybrid of MCE and EDGE architectures. We introduce partitions of different heights to a wide (EDGE-like) slit to establish optimal geometries for high-throughput droplet production. We demonstrate that the volume and monodispersity of the produced emulsion can be tuned solely by changing the height of these partitions. We show that the spacing of the partitions influences the size of the produced droplets, but not the population monodispersity. We also determine the moment of transition between two distinct droplet generation modes as a function of the geometrical parameters of the nozzle. The optimized grooved geometry appears to combine the advantages of both MCE and EDGE, i.e. spatial localization of droplet forming units (DFUs), high-throughput formation of tightly monodisperse droplets from parallel DFUs, and low sensitivity to variation in the flow rate of the dispersed phase. As a proof-of-concept we show grooved devices that for a 260-fold increase of flow rate produce droplets with volume increased by just 75%, as compared to 91% increase in volume over a 180-fold increase of flow rate of the dispersed phase in MCE devices. We also present the optimum microfluidic device geometry that almost doubles the throughput of an MCE device in the generation of nanoliter droplets.

There is a long-standing question of whether it is possible to extend the formalism of equilibrium thermodynamics to the case of nonequilibrium systems in steady-states. We have made such an extension for an ideal gas in a heat flow. Here, we investigated whether such a description exists for the system with interactions: the van der Waals gas in a heat flow. We introduced a steady-state fundamental relation and the parameters of state, each associated with a single way of changing energy. The first law of nonequilibrium thermodynamics follows from these parameters. The internal energy U for the nonequilibrium states has the same form as in equilibrium thermodynamics. For the van der Waals gas, $U(S^{*},V,N,a^{*},b^{*})$ is a function of only five parameters of state (irrespective of the number of parameters characterizing the boundary conditions): the effective entropy $S^{*}$, volume V, number of particles N, and rescaled van der Waals parameters $a^{*}$, $b^{*}$. The state parameters, $a^{*}$, $b^{*}$, together with $S^{*}$, determine the net heat exchange with the environment. The net heat differential does not have an integrating factor. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.